Many large-scale cross-sectional and longitudinal imaging studies have been or are being widely conducted to better understand the progress of neurodegenerative and neuropsychiatric disorders or the normal brain development. However, analysis of both cross-sectional and longitudinal imaging data has been hindered by the lack of advanced image processing and statistical tools for analyzing complex and correlated imaging data (e.g., diffusion tensor, deformation tensor, medial shape representation) in curved space along with behavioral and clinical data in Euclidean space. In response to PAR-07-070, the primary goal of this project is to develop new statistical tools and to evaluate these statistical tools for analysis of imaging data in curved space, in combination with behavioral and clinical information in Euclidean space obtained from both cross-sectional and longitudinal studies. As these tools are developed, they will be evaluated and refined through extensive Monte Carlo simulations and data analysis. Also, the efficacy of the tools developed under this grant will be tested by both simulated cross-sectional and longitudinal datasets and the two datasets including a longitudinal MRI study of schizophrenia and a longitudinal MRI study of autism, respectively. Moreover, the companion software for all developed statistical tools, once validated, will be disseminated to imaging researchers through http://www.nitrc.org/, as we did for our brain image registration algorithm called HAMMER. This analysis software will provide much needed imaging tools for analyzing complex, correlated imaging data in biomedical, behavioral, and social sciences. Thus, it is applicable to a variety of neuroimaging studies, e.g., on major neurodegenerative diseases, neuropsychiatric disorders, substance use disorders, and brain development.